Hydrological Theory

Derivation of the Huff Storm

Based on data from watersheds in the
mid-western USA, Huff (see References) suggested a family of
non-dimensional, storm distribution patterns. The events were divided
into four groups in which the peak rainfall intensity occurs in the
first, second, third or fourth quarter of the storm duration. Within
each group the distribution was plotted for different probabilities of
occurrence. MIDUSS uses the median curve for each of the four
quartile distributions. The non-dimensional curves are illustrated in
Figure 7-3 below and are tabulated in Table 7-1.

Figure 7-3 - Huff's four
storm distributions.

To define a storm of this type you must
provide values for the total depth of rainfall (in
millimetres or inches), the duration of
the storm (in minutes) and the quartile distribution required (i.e. 1,
2, 3 or 4). The duration must not exceed the maximum storm duration
defined in the Hydrology/Time parameters menu command and, as
with the Chicago storm option, an error message is displayed if this
constraint is violated. Once the parameter values have been entered
and confirmed by pressing the [Display] command button, the hyetograph
is displayed in both graphical and tabular form. You can experiment
by altering any of the data - even the type of storm - and re-using
the [Display] button until you press the [Accept] button to save the
storm and close the Storm command.

The four quartile Huff distributions are
approximated by a series of chords joining points defined by the
non-dimensional values in the table referenced below. Figure 7-4
shows a typical curve (not to scale) which for clarity uses only a
very small number of steps. The time base for the NH dimensionless
points defining the ‘curve’ is subdivided into dimensionless time
steps defined by:

where NH
= number of points defining the Huff curve (shown as NH
= 7 but usually much more)

NDT
= number of rainfall intensities required (shown as only 15 in Figure
7-4).

Figure 7-4 -
Discretization of a Huff curve.

The values of the dimensionless fractions
Pk and Pk+1
at the start and finish of each time-step are obtained by linear
interpolation and the corresponding rainfall intensity is then given
as:

where

For the example shown in Figure 7-4, the
Huff 2nd quartile curve is approximated by NH=7 points with
a storm duration which is divided into 15 time steps. Then Dt
= (7-1)/15 = 0.4. The calculation of the rainfall fractions Pk+1
required for eq. [7.10] is then carried
out as shown in the table below.